def plot_histogram(self, clr=(0,0,1), eps = 0.4):
r"""
Plot the histogram plot of the sequence.
The sequence is assumed to be real or from a finite field,
with a real indexing set ``I`` coercible into `\RR`.
Options are ``clr``, which is an RGB value, and ``eps``, which
is the spacing between the bars.
EXAMPLES::
sage: J = range(3)
sage: A = [ZZ(i^2)+1 for i in J]
sage: s = IndexedSequence(A,J)
sage: P = s.plot_histogram()
sage: show(P) # Not tested
"""
# elements must be coercible into RR
I = self.index_object()
N = len(I)
S = self.list()
P = [polygon([[RR(I[i])-eps,0],[RR(I[i])-eps,RR(S[i])],[RR(I[i])+eps,RR(S[i])],[RR(I[i])+eps,0],[RR(I[i]),0]], rgbcolor=clr) for i in range(N)]
T = [text(str(I[i]),(RR(I[i]),-0.8),fontsize=15,rgbcolor=(1,0,0)) for i in range(N)]
return sum(P) + sum(T)
def plot_histogram(self, clr=(0,0,1), eps = 0.4):
r"""
Plot the histogram plot of the sequence.
The sequence is assumed to be real or from a finite field,
with a real indexing set ``I`` coercible into `\RR`.
Options are ``clr``, which is an RGB value, and ``eps``, which
is the spacing between the bars.
EXAMPLES::
sage: J = range(3)
sage: A = [ZZ(i^2)+1 for i in J]
sage: s = IndexedSequence(A,J)
sage: P = s.plot_histogram()
sage: show(P) # Not tested
"""
# elements must be coercible into RR
I = self.index_object()
N = len(I)
S = self.list()
P = [polygon([[RR(I[i])-eps,0],[RR(I[i])-eps,RR(S[i])],[RR(I[i])+eps,RR(S[i])],[RR(I[i])+eps,0],[RR(I[i]),0]], rgbcolor=clr) for i in range(N)]
T = [text(str(I[i]),(RR(I[i]),-0.8),fontsize=15,rgbcolor=(1,0,0)) for i in range(N)]
return sum(P) + sum(T)
def plot_histogram(self, clr=(0, 0, 1), eps=0.4):
"""
Plots the histogram plot of the sequence, which is assumed to be real
or from a finite field, with a real indexing set I coercible into RR.
Options are clr, which is an RGB value, and eps, which is the spacing between the
bars.
EXAMPLES:
sage: J = range(3)
sage: A = [ZZ(i^2)+1 for i in J]
sage: s = IndexedSequence(A,J)
sage: P = s.plot_histogram()
Now type show(P) to view this in a browser.
"""
#from sage.plot.misc import text
F = self.base_ring() ## elements must be coercible into RR
I = self.index_object()
N = len(I)
S = self.list()
P = [
polygon([[RR(I[i]) - eps, 0], [
RR(I[i]) - eps, RR(S[i])
], [RR(I[i]) + eps, RR(S[i])], [RR(I[i]) + eps, 0], [RR(I[i]), 0]],
rgbcolor=clr) for i in range(N)
]
T = [
text(str(I[i]), (RR(I[i]), -0.8), fontsize=15, rgbcolor=(1, 0, 0))
for i in range(N)
]
return sum(P) + sum(T)
def plot(self, xrange, **options):
r"""
Plot this function.
The plot is intended to give an idea of the accuracy of the evaluations
that led to it. However, it may not be a rigorous enclosure of the graph
of the function.
EXAMPLES::
sage: from ore_algebra import *
sage: from ore_algebra.analytic.function import DFiniteFunction
sage: DiffOps, x, Dx = DifferentialOperators()
sage: f = DFiniteFunction(Dx^2 - x,
....: [1/(gamma(2/3)*3^(2/3)), -1/(gamma(1/3)*3^(1/3))])
sage: plot(f, (-10, 5), color='black')
Graphics object consisting of 1 graphics primitive
"""
mids = generate_plot_points(lambda x: self.approx(x, 20).mid(),
xrange,
plot_points=200)
ivs = [(x, self.approx(x, 20)) for x, _ in mids]
bounds = [(x, y.upper()) for x, y in ivs]
bounds += [(x, y.lower()) for x, y in reversed(ivs)]
options.setdefault('aspect_ratio', 'automatic')
g = plot.polygon(bounds, thickness=1, **options)
return g
def sector(ray1, ray2, **extra_options):
r"""
Plot a sector between ``ray1`` and ``ray2`` centered at the origin.
.. NOTE::
This function was intended for plotting strictly convex cones, so it
plots the smaller sector between ``ray1`` and ``ray2`` and, therefore,
they cannot be opposite. If you do want to use this function for bigger
regions, split them into several parts.
.. NOTE::
As of version 4.6 Sage does not have a graphic primitive for sectors in
3-dimensional space, so this function will actually approximate them
using polygons (the number of vertices used depends on the angle
between rays).
INPUT:
- ``ray1``, ``ray2`` -- rays in 2- or 3-dimensional space of the same
length;
- ``extra_options`` -- a dictionary of options that should be passed to
lower level plotting functions.
OUTPUT:
- a plot.
EXAMPLES::
sage: from sage.geometry.toric_plotter import sector
sage: print sector((1,0), (0,1))
Graphics object consisting of 1 graphics primitive
sage: print sector((3,2,1), (1,2,3))
Graphics3d Object
"""
ray1 = vector(RDF, ray1)
ray2 = vector(RDF, ray2)
r = ray1.norm()
if len(ray1) == 2:
# Plot an honest sector
phi1 = arctan2(ray1[1], ray1[0])
phi2 = arctan2(ray2[1], ray2[0])
if phi1 > phi2:
phi1, phi2 = phi2, phi1
if phi2 - phi1 > pi:
phi1, phi2 = phi2, phi1 + 2 * pi
return disk((0, 0), r, (phi1, phi2), **extra_options)
else:
# Plot a polygon, 30 vertices per radian.
vertices_per_radian = 30
n = ceil(arccos(ray1 * ray2 / r**2) * vertices_per_radian)
dr = (ray2 - ray1) / n
points = (ray1 + i * dr for i in range(n + 1))
points = [r / pt.norm() * pt for pt in points]
points.append(vector(RDF, 3))
return polygon(points, **extra_options)
def sector(ray1, ray2, **extra_options):
r"""
Plot a sector between ``ray1`` and ``ray2`` centered at the origin.
.. NOTE::
This function was intended for plotting strictly convex cones, so it
plots the smaller sector between ``ray1`` and ``ray2`` and, therefore,
they cannot be opposite. If you do want to use this function for bigger
regions, split them into several parts.
.. NOTE::
As of version 4.6 Sage does not have a graphic primitive for sectors in
3-dimensional space, so this function will actually approximate them
using polygons (the number of vertices used depends on the angle
between rays).
INPUT:
- ``ray1``, ``ray2`` -- rays in 2- or 3-dimensional space of the same
length;
- ``extra_options`` -- a dictionary of options that should be passed to
lower level plotting functions.
OUTPUT:
- a plot.
EXAMPLES::
sage: from sage.geometry.toric_plotter import sector
sage: sector((1,0), (0,1))
Graphics object consisting of 1 graphics primitive
sage: sector((3,2,1), (1,2,3))
Graphics3d Object
"""
ray1 = vector(RDF, ray1)
ray2 = vector(RDF, ray2)
r = ray1.norm()
if len(ray1) == 2:
# Plot an honest sector
phi1 = arctan2(ray1[1], ray1[0])
phi2 = arctan2(ray2[1], ray2[0])
if phi1 > phi2:
phi1, phi2 = phi2, phi1
if phi2 - phi1 > pi:
phi1, phi2 = phi2, phi1 + 2 * pi
return disk((0,0), r, (phi1, phi2), **extra_options)
else:
# Plot a polygon, 30 vertices per radian.
vertices_per_radian = 30
n = ceil(arccos(ray1 * ray2 / r**2) * vertices_per_radian)
dr = (ray2 - ray1) / n
points = (ray1 + i * dr for i in range(n + 1))
points = [r / pt.norm() * pt for pt in points]
points.append(vector(RDF, 3))
return polygon(points, **extra_options)
def plot_histogram(self, clr=(0,0,1),eps = 0.4):
"""
Plots the histogram plot of the sequence, which is assumed to be real
or from a finite field, with a real indexing set I coercible into RR.
Options are clr, which is an RGB value, and eps, which is the spacing between the
bars.
EXAMPLES:
sage: J = range(3)
sage: A = [ZZ(i^2)+1 for i in J]
sage: s = IndexedSequence(A,J)
sage: P = s.plot_histogram()
Now type show(P) to view this in a browser.
"""
#from sage.plot.misc import text
F = self.base_ring() ## elements must be coercible into RR
I = self.index_object()
N = len(I)
S = self.list()
P = [polygon([[RR(I[i])-eps,0],[RR(I[i])-eps,RR(S[i])],[RR(I[i])+eps,RR(S[i])],[RR(I[i])+eps,0],[RR(I[i]),0]], rgbcolor=clr) for i in range(N)]
T = [text(str(I[i]),(RR(I[i]),-0.8),fontsize=15,rgbcolor=(1,0,0)) for i in range(N)]
return sum(P)+sum(T)
